Volterra 적분 방정식
DSolveValue를 사용하여 볼테라 적분 방정식을 풉니다.
In[1]:=
![Click for copyable input](assets.ko/solve-a-volterra-integral-equation/In_90.png)
eqn = y[x] == x^3 + \[Lambda] \!\(
\*SubsuperscriptBox[\(\[Integral]\), \(0\), \(x\)]\(\((t - \ x)\) y[
t] \[DifferentialD]t\)\);
In[2]:=
![Click for copyable input](assets.ko/solve-a-volterra-integral-equation/In_91.png)
sol = DSolveValue[eqn, y[x], x]
Out[2]=
![](assets.ko/solve-a-volterra-integral-equation/O_45.png)
λ의 다양한 값에 대한 솔루션을 플롯합니다.
In[3]:=
![Click for copyable input](assets.ko/solve-a-volterra-integral-equation/In_92.png)
Plot[Table[sol, {\[Lambda], 1, 3, 0.5}] // Evaluate, {x, 0, 20}]
Out[3]=
![](assets.ko/solve-a-volterra-integral-equation/O_46.png)
약한 특이성을 가진 볼테라 적분 방정식을 풉니다.
In[4]:=
![Click for copyable input](assets.ko/solve-a-volterra-integral-equation/In_93.png)
eqn = y[x] == x^a - \!\(
\*SubsuperscriptBox[\(\[Integral]\), \(0\), \(x\)]\(
\*FractionBox[\(y[t]\),
SqrtBox[\(x - t\)]] \[DifferentialD]t\)\);
DSolveValue를 사용하여 솔루션의 식을 얻습니다.
In[5]:=
![Click for copyable input](assets.ko/solve-a-volterra-integral-equation/In_94.png)
sol = DSolveValue[eqn, y[x], x]
Out[5]=
![](assets.ko/solve-a-volterra-integral-equation/O_47.png)
해를 플롯합니다.
In[6]:=
![Click for copyable input](assets.ko/solve-a-volterra-integral-equation/In_95.png)
Plot[Table[sol, {a, 1, 4, 0.7}] // Evaluate, {x, 0, 2}]
Out[6]=
![](assets.ko/solve-a-volterra-integral-equation/O_48.png)